a. State and prove the generalization of Example 18.15 for a direct product with n factors.
b. Prove the Chinese Remainder Theorem: Let ai, bi, ∊ ℤ+ for i = 1,2, ...., n and let gcd(bi, bj) = 1 for i ≠ j. Then there exists X ∊ ℤ+ such that X = ai (mod bj) for i = 1. 2. ... n.
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